Journal article

Singular values and evenness symmetry in random matrix theory

Folkmar Bornemann, Peter J Forrester

FORUM MATHEMATICUM | WALTER DE GRUYTER GMBH | Published : 2016

Abstract

Complex Hermitian random matrices with a unitary symmetry can be distinguished by a weight function. When this is even, it is a known result that the distribution of the singular values can be decomposed as the superposition of two independent eigenvalue sequences distributed according to particular matrix ensembles with chiral unitary symmetry. We give decompositions of the distribution of singular values, and the decimation of the singular values - whereby only even, or odd, labels are observed - for real symmetric random matrices with an orthogonal symmetry, and even weight. This requires further specifying the functional form of the weight to one of three types - Gauss, symmetric Jacobi ..

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University of Melbourne Researchers

Grants

Awarded by DFG-Collaborative Research Center, "Discretization in Geometry and Dynamics"


Awarded by Australian Research Council


Funding Acknowledgements

The work of FB was supported by the DFG-Collaborative Research Center, TRR 109, "Discretization in Geometry and Dynamics". The work of PJF was supported by the Australian Research Council through the grant DP140102613.